
(/VERSIONCHECK 2) 

(DEFUN |PFOQ;torsion?;FdB;1| (|d| $) (QEQCAR (SPADCALL |d| (QREFELT $ 11)) 0)) 

(DEFUN |PFOQ;ratcurve| (|d| |modulus| |disc| $)
  (PROG (|m| |n| |p| |bad| |r| |bd| |s| |b| |h| |hh| |mn| |nm| |i|)
    (RETURN
     (SEQ
      (LETT |mn|
            (SPADCALL
             (LETT |nm|
                   (SPADCALL
                    (LETT |i| (SPADCALL |d| (QREFELT $ 15))
                          . #1=(|PFOQ;ratcurve|))
                    (QREFELT $ 17))
                   . #1#)
             (QREFELT $ 19))
            . #1#)
      (LETT |h|
            (SPADCALL
             (LETT |hh| (SPADCALL |nm| (+ |mn| 1) (QREFELT $ 22)) . #1#)
             (QREFELT $ 23))
            . #1#)
      (LETT |s|
            (QCAR
             (SPADCALL (SPADCALL (SPADCALL |hh| (QREFELT $ 25)) (QREFELT $ 26))
                       (LETT |b|
                             (SPADCALL
                              (SPADCALL (SPADCALL |nm| |mn| (QREFELT $ 22))
                                        (QREFELT $ 27))
                              (QREFELT $ 26))
                             . #1#)
                       (QREFELT $ 29)))
            . #1#)
      (LETT |bd| (SPADCALL (SPADCALL |i| (QREFELT $ 30)) (QREFELT $ 33)) . #1#)
      (LETT |r| (SPADCALL |s| |b| (QREFELT $ 35)) . #1#)
      (LETT |bad|
            (SPADCALL
             (LIST |disc| (SPADCALL |r| (QREFELT $ 36))
                   (SPADCALL |r| (QREFELT $ 37)) (* (QCAR |bd|) (QCDR |bd|))
                   (SPADCALL |h| (QREFELT $ 38)))
             (QREFELT $ 40))
            . #1#)
      (LETT |n|
            (|PFOQ;rat| |modulus| |d|
             (LETT |p| (SPADCALL |bad| (QREFELT $ 42)) . #1#) $)
            . #1#)
      (EXIT
       (COND ((EQL |n| 1) |n|)
             (#2='T
              (SEQ
               (LETT |m|
                     (|PFOQ;rat| |modulus| |d|
                      (SPADCALL (SPADCALL |p| |bad| (QREFELT $ 43))
                                (QREFELT $ 42))
                      $)
                     . #1#)
               (EXIT (COND ((EQL |n| |m|) |n|) (#2# 0))))))))))) 

(DEFUN |PFOQ;rat| (|pp| |d| |p| $)
  (PROG (|gf|)
    (RETURN
     (SEQ (LETT |gf| (|InnerPrimeField| |p|) |PFOQ;rat|)
          (EXIT
           (SPADCALL |d| |pp| (CONS #'|PFOQ;rat!0| (VECTOR |gf| $))
                     (|compiledLookupCheck| '|order|
                                            (LIST (LIST '|NonNegativeInteger|)
                                                  (LIST '|FiniteDivisor|
                                                        (LIST '|Fraction|
                                                              (LIST
                                                               '|Integer|))
                                                        (|devaluate| (ELT $ 6))
                                                        (|devaluate| (ELT $ 7))
                                                        (|devaluate|
                                                         (ELT $ 8)))
                                                  (|devaluate| (ELT $ 7))
                                                  (LIST '|Mapping|
                                                        (|devaluate| |gf|)
                                                        (LIST '|Fraction|
                                                              (LIST
                                                               '|Integer|))))
                                            (|ReducedDivisor|
                                             (|Fraction| (|Integer|)) (ELT $ 6)
                                             (ELT $ 7) (ELT $ 8) |gf|)))))))) 

(DEFUN |PFOQ;rat!0| (|z1| $$)
  (PROG ($ |gf|)
    (LETT $ (QREFELT $$ 1) . #1=(|PFOQ;rat|))
    (LETT |gf| (QREFELT $$ 0) . #1#)
    (RETURN
     (PROGN
      (SPADCALL
       (SPADCALL (SPADCALL |z1| (QREFELT $ 36))
                 (|compiledLookupCheck| '|coerce| (LIST '$ (LIST '|Integer|))
                                        |gf|))
       (SPADCALL (SPADCALL |z1| (QREFELT $ 37))
                 (|compiledLookupCheck| '|coerce| (LIST '$ (LIST '|Integer|))
                                        |gf|))
       (|compiledLookupCheck| '/ (LIST '$ '$ '$) |gf|)))))) 

(DEFUN |PFOQ;possibleOrder| (|d| $)
  (PROG (|r|)
    (RETURN
     (SEQ
      (COND
       ((OR (ZEROP (SPADCALL (QREFELT $ 45)))
            (EQL
             (QVSIZE (SPADCALL (SPADCALL |d| (QREFELT $ 15)) (QREFELT $ 17)))
             1))
        1)
       ('T
        (SEQ
         (LETT |r| (SPADCALL (SPADCALL (QREFELT $ 46)) (QREFELT $ 47))
               |PFOQ;possibleOrder|)
         (EXIT (|PFOQ;ratcurve| |d| |r| (SPADCALL |r| (QREFELT $ 48)) $))))))))) 

(DEFUN |PFOQ;order;FdU;5| (|d| $)
  (PROG (|n|)
    (RETURN
     (COND
      ((OR
        (ZEROP
         (LETT |n|
               (|PFOQ;possibleOrder|
                (LETT |d| (SPADCALL |d| (QREFELT $ 49))
                      . #1=(|PFOQ;order;FdU;5|))
                $)
               . #1#))
        (NULL
         (SPADCALL (SPADCALL (SPADCALL |n| |d| (QREFELT $ 50)) (QREFELT $ 49))
                   (QREFELT $ 51))))
       (CONS 1 "failed"))
      ('T (CONS 0 |n|)))))) 

(DEFUN |PFOQ;torsionIfCan;FdU;6| (|d| $)
  (PROG (|g| |n|)
    (RETURN
     (SEQ
      (COND
       ((ZEROP
         (LETT |n|
               (|PFOQ;possibleOrder|
                (LETT |d| (SPADCALL |d| (QREFELT $ 49))
                      . #1=(|PFOQ;torsionIfCan;FdU;6|))
                $)
               . #1#))
        (CONS 1 "failed"))
       (#2='T
        (SEQ
         (LETT |g|
               (SPADCALL
                (SPADCALL (SPADCALL |n| |d| (QREFELT $ 50)) (QREFELT $ 49))
                (QREFELT $ 53))
               . #1#)
         (EXIT
          (COND ((QEQCAR |g| 1) (CONS 1 "failed"))
                (#2# (CONS 0 (CONS |n| (QCDR |g|))))))))))))) 

(DEFUN |PointsOfFiniteOrderRational| (&REST #1=#:G1845)
  (PROG ()
    (RETURN
     (PROG (#2=#:G1846)
       (RETURN
        (COND
         ((LETT #2#
                (|lassocShiftWithFunction| (|devaluateList| #1#)
                                           (HGET |$ConstructorCache|
                                                 '|PointsOfFiniteOrderRational|)
                                           '|domainEqualList|)
                . #3=(|PointsOfFiniteOrderRational|))
          (|CDRwithIncrement| #2#))
         ('T
          (UNWIND-PROTECT
              (PROG1 (APPLY (|function| |PointsOfFiniteOrderRational;|) #1#)
                (LETT #2# T . #3#))
            (COND
             ((NOT #2#)
              (HREM |$ConstructorCache|
                    '|PointsOfFiniteOrderRational|))))))))))) 

(DEFUN |PointsOfFiniteOrderRational;| (|#1| |#2| |#3|)
  (PROG (|pv$| $ |dv$| DV$3 DV$2 DV$1)
    (RETURN
     (PROGN
      (LETT DV$1 (|devaluate| |#1|) . #1=(|PointsOfFiniteOrderRational|))
      (LETT DV$2 (|devaluate| |#2|) . #1#)
      (LETT DV$3 (|devaluate| |#3|) . #1#)
      (LETT |dv$| (LIST '|PointsOfFiniteOrderRational| DV$1 DV$2 DV$3) . #1#)
      (LETT $ (GETREFV 57) . #1#)
      (QSETREFV $ 0 |dv$|)
      (QSETREFV $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #1#))
      (|haddProp| |$ConstructorCache| '|PointsOfFiniteOrderRational|
                  (LIST DV$1 DV$2 DV$3) (CONS 1 $))
      (|stuffDomainSlots| $)
      (QSETREFV $ 6 |#1|)
      (QSETREFV $ 7 |#2|)
      (QSETREFV $ 8 |#3|)
      (SETF |pv$| (QREFELT $ 3))
      $)))) 

(MAKEPROP '|PointsOfFiniteOrderRational| '|infovec|
          (LIST
           '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|)
              (|local| |#3|) (|Union| 44 '"failed") (|FiniteDivisor| 34 6 7 8)
              |PFOQ;order;FdU;5| (|Boolean|) |PFOQ;torsion?;FdB;1|
              (|FractionalIdeal| 6 24 7 8) (0 . |ideal|) (|Vector| 8)
              (5 . |numer|) (|Integer|) (10 . |minIndex|) (15 . |One|)
              (19 . |One|) (23 . |elt|) (29 . |lift|) (|Fraction| 6)
              (34 . |norm|) (39 . |retract|) (44 . |retract|)
              (|Record| (|:| |primePart| $) (|:| |commonPart| $))
              (49 . |separate|) (55 . |denom|)
              (|Record| (|:| |den| 18) (|:| |gcdnum| 18))
              (|PointsOfFiniteOrderTools| 6 7) (60 . |badNum|) (|Fraction| 18)
              (65 . |resultant|) (71 . |numer|) (76 . |denom|) (81 . |badNum|)
              (|List| $) (86 . |lcm|) (|PositiveInteger|) (91 . |getGoodPrime|)
              (96 . *) (|NonNegativeInteger|) (102 . |genus|)
              (106 . |definingPolynomial|) (110 . |polyred|)
              (115 . |doubleDisc|) (120 . |reduce|) (125 . *)
              (131 . |principal?|) (|Union| 8 '"failed") (136 . |generator|)
              (|Record| (|:| |order| 44) (|:| |function| 8))
              (|Union| 54 '"failed") |PFOQ;torsionIfCan;FdU;6|)
           '#(|torsionIfCan| 141 |torsion?| 146 |order| 151) 'NIL
           (CONS (|makeByteWordVec2| 1 'NIL)
                 (CONS '#()
                       (CONS '#()
                             (|makeByteWordVec2| 56
                                                 '(1 10 14 0 15 1 14 16 0 17 1
                                                   16 18 0 19 0 6 0 20 0 7 0 21
                                                   2 16 8 0 18 22 1 8 7 0 23 1
                                                   8 24 0 25 1 24 6 0 26 1 8 24
                                                   0 27 2 6 28 0 0 29 1 14 6 0
                                                   30 1 32 31 6 33 2 6 34 0 0
                                                   35 1 34 18 0 36 1 34 18 0 37
                                                   1 32 18 7 38 1 18 0 39 40 1
                                                   32 41 18 42 2 18 0 41 0 43 0
                                                   8 44 45 0 8 7 46 1 32 7 7 47
                                                   1 32 18 7 48 1 10 0 0 49 2
                                                   10 0 18 0 50 1 10 12 0 51 1
                                                   10 52 0 53 1 0 55 10 56 1 0
                                                   12 10 13 1 0 9 10 11)))))
           '|lookupComplete|)) 
